Lenses for Curved Sensor Systems

ABSTRACT

The subject disclosure is directed towards lenses for curved surfaces, including multi-element lens assemblies. In one or more implementations, an object-side meniscus lens is coupled to an image/curved surface side subassembly including a biconvex lens. The subassembly may comprise a single biconvex lens or a biconvex lens coupled to a negative meniscus lens.

BACKGROUND

Contemporary lenses are designed/optimized to focus on a planar image surface. However, optical lens systems do not generally have their best focus on a planar imaging surface. For example, spherical lens systems tend to best focus on a roughly hemispherical surface, called the Petzval surface. Much of the complexity of lens design is in forcing the lens system to achieve best focus on a planar imaging surface, far away from the Petzval surface.

Developments in sensor technology have yielded somewhat low resolution curved sensors (with the resolution likely to increase in the future) that provide for improved quality of images. However, with such curved sensors, lenses optimized for planar image surfaces are inappropriate.

SUMMARY

This Summary is provided to introduce a selection of representative concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used in any way that would limit the scope of the claimed subject matter.

Briefly, one or more of various aspects of the subject matter described herein are directed towards multi-element lens assemblies. One example implementation comprises a refractive object-side element having a positive object-facing surface, and one or more lenses optically coupled to the object-side element and configured to focus light onto a curved surface. Another example implementation comprises an object-side subassembly having overall positive refraction, and an image-side subassembly optically coupled to the object-side subassembly. The image-side subassembly is configured to receive light from the object-side subassembly and focus the received light onto a curved surface.

Other advantages may become apparent from the following detailed description when taken in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which:

FIGS. 1-3 are representations of example two-element lens assemblies, each including an object-side positive meniscus lens and an image-side biconvex lens, according to one or more example implementations.

FIGS. 4-6 are representations of example three-element lens assemblies, each including an object-side meniscus lens and an image-side subassembly comprising a biconvex lens and negative meniscus lens, according to one or more example implementations.

FIGS. 7-13 are representations of example four-element lens assemblies, each including an object-side positive refractive lens and an image-side negative refractive lens, according to one or more example implementations.

FIG. 14 is block diagram exemplifying a multiple lens assembly incorporated into a camera having a curved sensing surface, according to one or more example implementations

DETAILED DESCRIPTION

Various aspects of the technology described herein are generally directed towards multiple lens (multi-lens) assemblies configured to focus on a curved surface, such as a hemispherical or substantially hemispherical surface, e.g., a curved sensor. Two, three and four element multi-lens assemblies are exemplified herein, however it is understood that multi-lens assemblies having more than four elements, up to any practical number, are feasible. Further, wherever two or more lenses as shown as physically coupled, it is feasible to have a single lens ground, molded or otherwise manufactured as a single element provided that the materials were the same.

It should be understood that any of the examples herein are non-limiting. For instance, any of the refractive optical elements shown herein may be made of any suitable material, e.g., glass or plastic, and such materials may be used alone or in any combination in any lens assembly. Further, one or more reflective elements may be present instead of or in addition to refractive optical elements. As such, the present invention is not limited to any particular embodiments, aspects, concepts, structures, functionalities or examples described herein. Rather, any of the embodiments, aspects, concepts, structures, functionalities or examples described herein are non-limiting, and the present invention may be used various ways that provide benefits and advantages in lens technology in general.

FIG. 1 shows an example two-element refractive optical element assembly 100 including a refractive optical element (e.g., a generally positive meniscus lens 102) having a positive refractive power from the object-to image direction via a convex-object side surface and concave opposite side. As generally represented in FIG. 1, the convex object-facing side of the lens 102 has a larger radius of curvature than the opposite image-facing concave side. Note that FIG. 1 is not intended to convey any actual sizes or dimensions.

The positive meniscus lens 102 is coupled to a generally biconvex lens 104 to focus light onto a curved surface 108. As can be seen in FIG. 1, the lens 104 is configured to receive light from the lens 102. The lens 104 has an object-facing side with a smaller radius of curvature than its image/curved surface-facing side.

The lenses 102 and 104 are shown as physically coupled, however it is understood that they may be separated by a suitable gap filled with any liquid or gas, including air. The lenses 102 and 104 may be made of plastic, glass, or one plastic, one glass, for example. The following show data of one example implementation corresponding to FIG. 1:

Surf Type Radius Thickness Diameter Conic OBJ STAN- Infinity Infinity 0 0 DARD STO EVENASPH 2.149059 1.143113 1.477866 0.3033693 2 EVENASPH 0.5794461 1.250096 2.454417 −0.8047933 3 EVENASPH −2.715948 2.577189 2.676481 −0.7515823 IMA STAN- −4.180481 4.085812 −0.4251225 IMA DARD Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 −0.098497123 Coefficient on r{circumflex over ( )} 4 −0.040043231 Coefficient on r{circumflex over ( )} 6 0.026768729 Coefficient on r{circumflex over ( )} 8 −0.061589691 Coefficient on r{circumflex over ( )} 10 0.041752082 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.45158306 Coefficient on r{circumflex over ( )} 4 −0.014772696 Coefficient on r{circumflex over ( )} 6 −0.28951155 Coefficient on r{circumflex over ( )} 8 0.19693689 Coefficient on r{circumflex over ( )} 10 −0.089640559 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.03789558 Coefficient on r{circumflex over ( )} 4 −0.0063094918 Coefficient on r{circumflex over ( )} 6 0.0026530481 Coefficient on r{circumflex over ( )} 8 −0.0048491677 Coefficient on r{circumflex over ( )} 10 0.0027909406 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

FIG. 2 is similar to FIG. 1, and thus shows a two-element assembly 200 having a positive meniscus lens 222 is coupled to a generally biconvex lens 224 to focus light onto a curved surface 228. Differences between FIG. 1 and FIG. 2 include the thicknesses of the lenses 222 and 224, as well as the ratio of each assembly's elements' thicknesses.

The following show data of one example implementation corresponding to FIG. 2:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 STO EVENASPH 6.432122 1.799185 1.79147 0 2 EVENASPH 4.164469 1.833238 2.654085 0. 3 EVENASPH −5.779919 2.572927 3.290749 0 IMA STANDARD −4.979109 4.4 −0.1449482 IMA Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.016949412 Coefficient on r{circumflex over ( )} 4 −0.0060254369 Coefficient on r{circumflex over ( )} 6 0.002018416 Coefficient on r{circumflex over ( )} 8 −0.003288917 Coefficient on r{circumflex over ( )} 10 0.0013935683 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.10488576 Coefficient on r{circumflex over ( )} 4 0.0080114777 Coefficient on r{circumflex over ( )} 6 −0.013581529 Coefficient on r{circumflex over ( )} 8 0.0040498405 Coefficient on r{circumflex over ( )} 10 −0.00072005712 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.064406122 Coefficient on r{circumflex over ( )} 4 −0.0011588418 Coefficient on r{circumflex over ( )} 6 −0.00049122944 Coefficient on r{circumflex over ( )} 8 0.00020124711 Coefficient on r{circumflex over ( )} 10 2.7372079e−005 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

FIG. 3 is similar to FIGS. 1 and 2, having a two-element assembly 300 with a positive (object-side) meniscus lens 332 is coupled to a generally biconvex lens 334 to focus light onto a curved surface 338. The following show data of one example implementation corresponding to FIG. 3:

Surf Type Radius Thickness Diameter Conic OBJ STAN- Infinity Infinity 0 0 DARD STO EVENASPH 1.91288 1.110882 1.623566 −0.1702735 2 EVENASPH 0.4475397 1.378157 2.557306 −0.8949009 3 EVENASPH −2.76981 2.49896 2.797017 −0.7235262 IMA STAN- −4.156886 4 −0.4313463 IMA DARD Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 −0.11783356 Coefficient on r{circumflex over ( )} 4 −0.03550621 Coefficient on r{circumflex over ( )} 6 0.02213866 Coefficient on r{circumflex over ( )} 8 −0.043313454 Coefficient on r{circumflex over ( )} 10 0.024704316 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.7091958 Coefficient on r{circumflex over ( )} 4 0.0034960593 Coefficient on r{circumflex over ( )} 6 −0.31902203 Coefficient on r{circumflex over ( )} 8 0.1978099 Coefficient on r{circumflex over ( )} 10 −0.078643857 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.035138687 Coefficient on r{circumflex over ( )} 4 −0.0051648925 Coefficient on r{circumflex over ( )} 6 0.0030843072 Coefficient on r{circumflex over ( )} 8 −0.0044482251 Coefficient on r{circumflex over ( )} 10 0.002190287 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

In the two-element design, in general there is a high negative conic constant, and hence large relative asphericity. Correction of coma and astigmatism may be done as with the three-element design as described below, and is generally based upon the surfaces remote from the stop and solving simultaneously for zero S_(II) and S_(III):

0=S _(II)+ε₂ ·S* _(I2)+ε₃ ·S* _(I3)

0=S _(III)+ε₂ ² ·S* _(I2)+ε₃ ² ·S* _(I3)

where S_(II) and S_(III) are the coma and astigmatism terms of the whole system before correction, respectively, ε₂ and ε₃ are the ratio of the principal and marginal ray heights at the second and third surfaces and S_(I2)* and S_(I3)* are the additional spherical aberration terms at the second and third surfaces.

Given the relative size of the Δn at those boundaries for optical materials used in the visible, it is apparent that the actual asphericity in terms of surface sag needs to be larger at surface two than at surface three.

FIG. 4 shows a three-element assembly 440 having an object-side positive, generally meniscus lens 442 optically coupled to a generally biconvex intermediate lens 444. In turn, the intermediate lens 444 is coupled (e.g., physically or at least optically) to a generally negative meniscus lens-shaped lens 446, which focuses light onto the curved surface 448.

Although as in FIGS. 1-3, no sizes or dimensions are intended to be conveyed in FIG. 4, although the relative radii of curvature of the individual elements and the gaps are such that the focal lengths are appropriate. The following show data of one example implementation corresponding to FIG. 4:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 STO EVENASPH 6.644491 0.9350005 4.586162 2.190639 2 EVENASPH 8.539573 1.159836 4.023222 10.7804 3 EVENASPH 4.935623 1.153228 2.607965 −4.112604 4 EVENASPH −3.927883 0.9223948 2.604223 −0.2457859 5 EVENASPH −4.481268 2.140144 3.366548 −3.722884 IMA STANDARD −4.128595 4.4 0.113461 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 0.067316768 Coefficient on r{circumflex over ( )} 4 0.0013146276 Coefficient on r{circumflex over ( )} 6 0.00035928207 Coefficient on r{circumflex over ( )} 8 −1.936854e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.0017789485 Coefficient on r{circumflex over ( )} 4 0.0013930933 Coefficient on r{circumflex over ( )} 6 3.0658734e−005 Coefficient on r{circumflex over ( )} 8 −9.2314671e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.042529249 Coefficient on r{circumflex over ( )} 4 0.00303047 Coefficient on r{circumflex over ( )} 6 0.0044255189 Coefficient on r{circumflex over ( )} 8 −0.00060161924 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.36101226 Coefficient on r{circumflex over ( )} 4 −0.025921905 Coefficient on r{circumflex over ( )} 6 −0.0023854566 Coefficient on r{circumflex over ( )} 8 0.0022634492 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 5 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.07956166 Coefficient on r{circumflex over ( )} 4 0.0021746083 Coefficient on r{circumflex over ( )} 6 6.0171164e−006 Coefficient on r{circumflex over ( )} 8 0.00059107681 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

FIG. 5 shows an embodiment of another three-element assembly 550. The object-side lens 552 is close to plano-convex, but is still somewhat of a generally a positive meniscus lens. The biconvex lens 554 receives light from the object-side lens 552, and is shown as being physically coupled to a negative meniscus lens 556, which focuses the light onto the curved surface 558.

The following show data of one example implementation corresponding to FIG. 5:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 STO EVENASPH 10.04376 2.500336 5.938842 −2.612775 2 EVENASPH 12.47944 0.7280293 3.826284 18.71383 3 EVENASPH 5.209887 1.091996 2.482273 −1.745061 4 EVENASPH −2.867931 1.300414 2.532966 −1.174326 5 EVENASPH −5.473922 1.711776 3.566488 4.812232 IMA STANDARD −4.024843 4.4 0.457535 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 0.062615788 Coefficient on r{circumflex over ( )} 4 0.00059644135 Coefficient on r{circumflex over ( )} 6 9.8295376e−006 Coefficient on r{circumflex over ( )} 8 −9.0673164e−006 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.012678592 Coefficient on r{circumflex over ( )} 4 −0.00047655241 Coefficient on r{circumflex over ( )} 6 −0.00079881155 Coefficient on r{circumflex over ( )} 8 5.0952505e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.036716283 Coefficient on r{circumflex over ( )} 4 0.00017478943 Coefficient on r{circumflex over ( )} 6 0.001604258 Coefficient on r{circumflex over ( )} 8 −0.00029375864 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.2496809 Coefficient on r{circumflex over ( )} 4 −0.04802043 Coefficient on r{circumflex over ( )} 6 −0.037620033 Coefficient on r{circumflex over ( )} 8 0.023786848 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 5 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.071578632 Coefficient on r{circumflex over ( )} 4 0.0054829717 Coefficient on r{circumflex over ( )} 6 0.00016838389 Coefficient on r{circumflex over ( )} 8 0.00044381629 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

FIG. 6 shows an embodiment of another three-element assembly 660. The object-side lens 662 is a generally positive meniscus lens. A biconvex lens 664 receives light from the object-side lens 662, and is shown as being physically coupled to a negative meniscus lens 666, which focuses the light onto the curved surface 668.

The following show data of one example implementation corresponding to FIG. 6:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 STO EVENASPH 2.982782 1.579595 4.635227 0 2 EVENASPH 8.397587 0.6721739 3.783354 0 3 EVENASPH 3.775295 1.038479 2.383311 0 4 EVENASPH −1.307395 0.8361284 2.462342 0 5 EVENASPH −2.109334 1.640701 3.354517 0 IMA STANDARD −3.623487 3.992889 0.2323074 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 0.026790834 Coefficient on r{circumflex over ( )} 4 0.001466062 Coefficient on r{circumflex over ( )} 6 0.00018799414 Coefficient on r{circumflex over ( )} 8 1.1263726e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0075103766 Coefficient on r{circumflex over ( )} 4 0.0044773476 Coefficient on r{circumflex over ( )} 6 −0.00096070056 Coefficient on r{circumflex over ( )} 8 8.9569244e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0082692559 Coefficient on r{circumflex over ( )} 4 −0.0035430794 Coefficient on r{circumflex over ( )} 6 −0.0047729108 Coefficient on r{circumflex over ( )} 8 0.0037146523 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 0.012763776 Coefficient on r{circumflex over ( )} 4 0.021906493 Coefficient on r{circumflex over ( )} 6 0.0034661071 Coefficient on r{circumflex over ( )} 8 0.010609723 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0 Surface 5 EVENASPH Coefficient on r{circumflex over ( )} 2 0.046717901 Coefficient on r{circumflex over ( )} 4 0.0094163635 Coefficient on r{circumflex over ( )} 6 0.0016692686 Coefficient on r{circumflex over ( )} 8 −8.2571674e−005 Coefficient on r{circumflex over ( )} 10 0 Coefficient on r{circumflex over ( )} 12 0 Coefficient on r{circumflex over ( )} 14 0 Coefficient on r{circumflex over ( )} 16 0

FIGS. 7-13 are examples of four element lens assemblies. As can be seen, each of these example lens assemblies has a lens closet to the curved sensor that is a negative meniscus lens, (although in the examples of FIG. 12 and FIG. 13 the lenses are close to plano-concave). For purposes of brevity, rather than describe the individual lenses in each of the exemplified four-element lens assemblies, the data for each is provided.

The following show data of one example implementation corresponding to FIG. 7:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 224.3738 18.41708 95.81648 −11.33441 2 EVENASPH 273.4945 42.98881 81.69407 32.00641 3 EVENASPH −231.447 13.22963 47.1052 −480.5678 STO EVENASPH 81.19232 7.7093 11.33238 −73.30876 5 EVENASPH −33.06094 4.035196 12.72217 17.45717 6 EVENASPH −27.76914 20.93704 17.26029 4.856911 IMA STANDARD −29.79523 32 0.2489563 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 0.0009050068 Coefficient on r{circumflex over ( )} 4 −1.2866628e−007 Coefficient on r{circumflex over ( )} 6 −2.9977403e−011 Coefficient on r{circumflex over ( )} 8  −6.285853e−016 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.0016432507 Coefficient on r{circumflex over ( )} 4  −5.968454e−007 Coefficient on r{circumflex over ( )} 6 −5.8903375e−011 Coefficient on r{circumflex over ( )} 8 −2.4605836e−014 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0027362957 Coefficient on r{circumflex over ( )} 4   1.7252281e−006 Coefficient on r{circumflex over ( )} 6 −1.9753377e−009 Coefficient on r{circumflex over ( )} 8   4.4952875e−013 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.0061035575 Coefficient on r{circumflex over ( )} 4 −1.1573733e−005 Coefficient on r{circumflex over ( )} 6 −3.8576759e−007 Coefficient on r{circumflex over ( )} 8   3.8540073e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 5 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.048220655 Coefficient on r{circumflex over ( )} 4 −0.00017573318 Coefficient on r{circumflex over ( )} 6 −8.9580864e−007 Coefficient on r{circumflex over ( )} 8 −2.3634797e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.022321611 Coefficient on r{circumflex over ( )} 4 −2.5698424e−005 Coefficient on r{circumflex over ( )} 6 −1.2705637e−008 Coefficient on r{circumflex over ( )} 8   5.0233863e−010 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 8 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 162.123 32.50005 119.0927 3.010826 2 EVENASPH 129.3732 34.26242 81.72527 4.196508 3 EVENASPH 32.65833 5.173827 23.27261 −2.239026 4 EVENASPH 51.06849 3.007101 19.19739 −5.892531 STO EVENASPH 31.85256 5.302895 10.03037 24.96704 6 EVENASPH −24.50952 4.964779 9.685754 20.14663 7 EVENASPH −27.137 14.95837 15.27177 −6.28567 IMA STANDARD −24.65858 32 0.3400413 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 0.00026574669 Coefficient on r{circumflex over ( )} 4 1.3090292e−007 Coefficient on r{circumflex over ( )} 6 −8.067507e−011 Coefficient on r{circumflex over ( )} 8 3.2095808e−015 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.00084216787 Coefficient on r{circumflex over ( )} 4 6.1215846e−007 Coefficient on r{circumflex over ( )} 6 −5.3812441e−010   Coefficient on r{circumflex over ( )} 8 3.5072263e−014 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.0092935737 Coefficient on r{circumflex over ( )} 4 −5.5951183e−006   Coefficient on r{circumflex over ( )} 6 −7.2230948e−008   Coefficient on r{circumflex over ( )} 8 −7.3651341e−010   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0024420196 Coefficient on r{circumflex over ( )} 4 −2.2371721e−006   Coefficient on r{circumflex over ( )} 6 −8.2333791e−008   Coefficient on r{circumflex over ( )} 8 −4.4480187e−010   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.0097938162 Coefficient on r{circumflex over ( )} 4 −2.3705972e−006   Coefficient on r{circumflex over ( )} 6  4.256789e−007 Coefficient on r{circumflex over ( )} 8 −1.4665789e−010   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.073096589 Coefficient on r{circumflex over ( )} 4 5.7190799e−005 Coefficient on r{circumflex over ( )} 6 4.6297098e−007 Coefficient on r{circumflex over ( )} 8 −1.1106303e−009   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.014538394 Coefficient on r{circumflex over ( )} 4 4.4184008e−005 Coefficient on r{circumflex over ( )} 6 3.8845346e−007 Coefficient on r{circumflex over ( )} 8 3.6819816e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 9 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 62.96768 44.60342 66.41456 0.3010589 2 EVENASPH 31.11318 0.7130898 27.68156 1.258264 3 EVENASPH 24.76477 14.99275 26.88566 1.960634 4 EVENASPH 115.5418 0.1125 19.6447 107.2977 STO EVENASPH 38.72699 10.74507 17.99032 10.32326 6 EVENASPH −17.98552 3.940343 18.76694 2.402588 7 EVENASPH −26.68607 10.7144 22.89597 2.670887 IMA STANDARD −21.95436 21.99506 0.4361121 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0027228227 Coefficient on r{circumflex over ( )} 4   2.7447576e−007 Coefficient on r{circumflex over ( )} 6 −8.0962734e−011 Coefficient on r{circumflex over ( )} 8 −1.1754249e−013 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.00080108496 Coefficient on r{circumflex over ( )} 4   1.7707049e−005 Coefficient on r{circumflex over ( )} 6   1.2244301e−008 Coefficient on r{circumflex over ( )} 8   1.5406142e−010 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.010033911 Coefficient on r{circumflex over ( )} 4   9.1856009e−006 Coefficient on r{circumflex over ( )} 6 −7.4005883e−009 Coefficient on r{circumflex over ( )} 8 −2.3732676e−011 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.014248381 Coefficient on r{circumflex over ( )} 4   2.4639797e−005 Coefficient on r{circumflex over ( )} 6 −3.0974358e−007 Coefficient on r{circumflex over ( )} 8   2.1326118e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.0031486196 Coefficient on r{circumflex over ( )} 4  −6.719473e−006 Coefficient on r{circumflex over ( )} 6 −4.2952055e−007 Coefficient on r{circumflex over ( )} 8   2.3378143e−010 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.024585082 Coefficient on r{circumflex over ( )} 4 −0.00015759285 Coefficient on r{circumflex over ( )} 6   7.5876778e−007 Coefficient on r{circumflex over ( )} 8 −1.7075289e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.012329076 Coefficient on r{circumflex over ( )} 4 −1.0162983e−005 Coefficient on r{circumflex over ( )} 6   1.9008622e−007 Coefficient on r{circumflex over ( )} 8 −5.7975021e−010 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 10 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 15.48462 6.4366753 18.01328 0.7350255 2 EVENASPH 8.848879 0.55726 11.00158 1.003955 3 EVENASPH 9.032038 6.399996 10.93563 1.201861 4 EVENASPH 52.28122 0.6596292 8.418669 −102.507 STO EVENASPH 11.75226 4.029279 5.893034 7.760635 6 EVENASPH −5.062495 1.4752 6.311816 0.8644125 7 EVENASPH −9.769045 3.78492 7.504619 0.3084521 IMA STANDARD −8.85309 8.334322 0.4148249 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0071907745 Coefficient on r{circumflex over ( )} 4   3.5659214e−005 Coefficient on r{circumflex over ( )} 6 −6.2172173e−008 Coefficient on r{circumflex over ( )} 8 −4.0974779e−009 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0088366866 Coefficient on r{circumflex over ( )} 4 0.00040564053 Coefficient on r{circumflex over ( )} 6   9.3202089e−007 Coefficient on r{circumflex over ( )} 8 −1.0213473e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.017895107 Coefficient on r{circumflex over ( )} 4 0.00040857664 Coefficient on r{circumflex over ( )} 6 −3.2173946e−006 Coefficient on r{circumflex over ( )} 8 −3.0588291e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.038343155 Coefficient on r{circumflex over ( )} 4 0.00049343981 Coefficient on r{circumflex over ( )} 6 −2.6827802e−005 Coefficient on r{circumflex over ( )} 8   7.0872313e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.0057852056 Coefficient on r{circumflex over ( )} 4 0.00020538583 Coefficient on r{circumflex over ( )} 6 −3.5523241e−005 Coefficient on r{circumflex over ( )} 8 −1.8504176e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.070725522 Coefficient on r{circumflex over ( )} 4 −0.001121991 Coefficient on r{circumflex over ( )} 6   5.9885948e−005 Coefficient on r{circumflex over ( )} 8   8.3858477e−006 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.019022298 Coefficient on r{circumflex over ( )} 4 0.00011123481 Coefficient on r{circumflex over ( )} 6   2.6657465e−005 Coefficient on r{circumflex over ( )} 8 −2.3693164e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 11 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 34.46149 21.6879 36.8607 0 2 EVENASPH 22.25803 3.200012 18.05265 0 3 EVENASPH −43.37931 15.34823 17.64078 0 4 EVENASPH −15.71166 3.197076 12.67488 0 STO EVENASPH 33.63017 7.563545 6.623186 0 6 EVENASPH −9.632602 6.408138 9.044731 0 7 EVENASPH −25.75564 9.774625 12.14408 0 IMA STANDARD −24.33541 16.11549 0 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0023330882 Coefficient on r{circumflex over ( )} 4 −2.0063176e−006   Coefficient on r{circumflex over ( )} 6  1.712178e−009 Coefficient on r{circumflex over ( )} 8 −4.8168342e−012   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.0039164919 Coefficient on r{circumflex over ( )} 4 8.2553246e−006 Coefficient on r{circumflex over ( )} 6 2.4164262e−007 Coefficient on r{circumflex over ( )} 8 3.8123788e−010 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.012882344 Coefficient on r{circumflex over ( )} 4 −5.6454175e−005   Coefficient on r{circumflex over ( )} 6 3.7235058e−007 Coefficient on r{circumflex over ( )} 8 −2.5203063e−009   Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0052614684 Coefficient on r{circumflex over ( )} 4 0.0001875086 Coefficient on r{circumflex over ( )} 6 −2.2633249e−006   Coefficient on r{circumflex over ( )} 8 1.5881566e−008 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.0034148683 Coefficient on r{circumflex over ( )} 4 0.00026669857 Coefficient on r{circumflex over ( )} 6 −4.7164879e−006   Coefficient on r{circumflex over ( )} 8 8.4829314e−008 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.016533876 Coefficient on r{circumflex over ( )} 4 −0.00028941833 Coefficient on r{circumflex over ( )} 6 −1.0187295e−005   Coefficient on r{circumflex over ( )} 8 9.2891838e−007 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.0062723283 Coefficient on r{circumflex over ( )} 4  4.010936e−005 Coefficient on r{circumflex over ( )} 6 6.2071785e−007 Coefficient on r{circumflex over ( )} 8 1.0114067e−008 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 12 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 7.057435 2.988707 5.674679 1.814324 2 EVENASPH 3.258223 0.08128771 3.426519 −0.5657294 3 EVENASPH 2.901909 0.9694701 3.392434 0.05291388 4 EVENASPH −31.11675 0 3.368211 0 STO EVENASPH 2.944861 1.764741 2.528473 −0.3409325 6 EVENASPH −1.574102 0.3459662 2.519126 −1.902648 7 EVENASPH −5.186811 1.116115 2.59444 −28.09088 IMA STANDARD −3.470872 3.036393 0.2865449 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.032551323 Coefficient on r{circumflex over ( )} 4 −0.0048517168 Coefficient on r{circumflex over ( )} 6 −0.00019793491 Coefficient on r{circumflex over ( )} 8 1.3280715e−005 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.028308733 Coefficient on r{circumflex over ( )} 4 −0.002587907 Coefficient on r{circumflex over ( )} 6 0.0076772372 Coefficient on r{circumflex over ( )} 8 −0.0013908962 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.052136909 Coefficient on r{circumflex over ( )} 4 −0.0025480509 Coefficient on r{circumflex over ( )} 6 0.0063986009 Coefficient on r{circumflex over ( )} 8 −0.00051891927 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.055267632 Coefficient on r{circumflex over ( )} 4 0.0010476998 Coefficient on r{circumflex over ( )} 6 0.0031384482 Coefficient on r{circumflex over ( )} 8 −0.00032573638 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.052303764 Coefficient on r{circumflex over ( )} 4 0.0013254458 Coefficient on r{circumflex over ( )} 6 0.011041063 Coefficient on r{circumflex over ( )} 8 −0.0042722676 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.12060363 Coefficient on r{circumflex over ( )} 4 0.032302384 Coefficient on r{circumflex over ( )} 6 −0.032302727 Coefficient on r{circumflex over ( )} 8 −0.0035113698 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 0.015231714 Coefficient on r{circumflex over ( )} 4 0.012736379 Coefficient on r{circumflex over ( )} 6 0.005512558 Coefficient on r{circumflex over ( )} 8 0.0040815702 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 13 example lens assembly details:

Surf Type Radius Thickness Diameter Conic OBJ STANDARD Infinity Infinity 0 0 1 EVENASPH 5.859769 1.839874 3.996322 −0.0417652 2 EVENASPH 2.831865 0.2170869 2.506635 −0.5090163 3 EVENASPH 2.306807 0.5873021 2.334853 0.5058974 4 EVENASPH 80.21697 0.1369206 2.228267 4182.971 STO EVENASPH 3.152057 1.341948 1.701928 −1.099714 6 EVENASPH −1.410627 0.3361722 1.949082 −1.114667 7 EVENASPH −4.960287 1.375117 2.223864 −21.00731 IMA STANDARD −3.508075 3.001053 0 IMA Surface 1 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.02899649 Coefficient on r{circumflex over ( )} 4 −0.010051793 Coefficient on r{circumflex over ( )} 6 −0.00048326198 Coefficient on r{circumflex over ( )} 8 9.7659737e−005 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 2 EVENASPH Coefficient on r{circumflex over ( )} 2 0.024143729 Coefficient on r{circumflex over ( )} 4 −0.00055718234 Coefficient on r{circumflex over ( )} 6 0.0058160331 Coefficient on r{circumflex over ( )} 8 −0.0023649112 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 3 EVENASPH Coefficient on r{circumflex over ( )} 2 0.049071226 Coefficient on r{circumflex over ( )} 4 0.0097786873 Coefficient on r{circumflex over ( )} 6 0.0089052798 Coefficient on r{circumflex over ( )} 8 0.0023761706 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 4 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.050967198 Coefficient on r{circumflex over ( )} 4 0.0062549297 Coefficient on r{circumflex over ( )} 6 0.013279928 Coefficient on r{circumflex over ( )} 8 −0.0047169231 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface STO EVENASPH Coefficient on r{circumflex over ( )} 2 0.036069468 Coefficient on r{circumflex over ( )} 4 −0.0019326477 Coefficient on r{circumflex over ( )} 6 0.010929391 Coefficient on r{circumflex over ( )} 8 −0.019845718 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 6 EVENASPH Coefficient on r{circumflex over ( )} 2 −0.04959238 Coefficient on r{circumflex over ( )} 4 −0.03986785 Coefficient on r{circumflex over ( )} 6 −0.040731282 Coefficient on r{circumflex over ( )} 8 0.012511117 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0 Surface 7 EVENASPH Coefficient on r{circumflex over ( )} 2 0.022642757 Coefficient on r{circumflex over ( )} 4 0.010081191 Coefficient on r{circumflex over ( )} 6 0.013106754 Coefficient on r{circumflex over ( )} 8 0.00031467056 Coefficient on r{circumflex over ( )}10 0 Coefficient on r{circumflex over ( )}12 0 Coefficient on r{circumflex over ( )}14 0 Coefficient on r{circumflex over ( )}16 0

FIG. 14 shows an example of a camera 1440 containing a lens assembly 1442 constructed in accordance with the technology described herein. As can be seen, lens subassemblies 1446 ₁-1446 _(n) focus light, which may be visible light and/or other light (such as infrared) onto a curved surface 1448.

ADDITIONAL EXAMPLE DETAILS

In general, some of the exemplified designs are relatively wide-aperture and wide-field and may be constructed using high-order aspheres. Designs may be re-optimized for a lower aperture, and higher-order terms may be dropped. This brings the designs within reach of a description using first-order and third-order wavefront expansions—the domain in which Seidel aberration analysis is appropriate and hence enables the optical function of the various surfaces to be explained.

The lens elements are in general thick in comparison to their separation and therefore a thin-lens solution is not appropriate.

Seidel Correction aberration Comment needed S_(I) Spherical aberration Yes S_(II) Coma Yes S_(III) Astigmatism Yes S_(IV) Petzval sum (field No curvature if S_(III) = 0) S_(V) Distortion No* C_(I) Longitudinal chromatic aberration Yes C_(II) Transverse chromatic aberration Yes

In these designs, field curvature is effectively left to float and the image sensor is placed at the Petzval surface. Note that distortion correction is desirable in principle, but the effect of correcting distortion is to flatten the image field and hence negate some of the benefits of the curved image field so it is left uncorrected.

Note that even without the aspheres, the system at moderate apertures is well-corrected for the first three primary monochromatic aberrations. The primary offender is astigmatism, and there are only a few wavelengths of this at f/4; by comparison a thin-lens of similar power at the stop would have about 21 wavelengths of astigmatism. Low starting aberrations tend to be helpful to the design.

In one aspect, the design is pseudo-symmetric, which makes coma and transverse color low by default. The design is also generally pseudo-centro-symmetric, which makes coma and astigmatism low at the external surfaces of the lens (the principal ray is roughly normal to the surface).

One or more implementations start with a positive curvature (as with most lenses), as well as having the first element overall positive to help minimize total track. One or more implementations use one aplanatic surface before the stop and/or in which the marginal ray is close to normal at this surface, and make the surface at the stop nearly concentric with the preceding surface. The curvature may be used to control astigmatism as desired.

The buried surface both corrects for longitudinal color and introduces overcorrected (negative) spherical aberration, which helps compensate for that at the external surfaces of the lens.

If an implementation allows aspheres, astigmatism maybe corrected by introducing an asphere into a surface remote from the stop. The effect of the asphere is to introduce a spherical aberration term that, dependent on the ratio of the principal ray height to the marginal ray height will correct some or all of the astigmatism. However, there is likely some coma. Because this was already low, this additional coma is corrected in another surface.

Correcting the residual spherical aberration can be done by an asphere at the stop. One basic approach finds a Gaussian solution that gives low lateral and longitudinal color, ignoring field curvature but using some of the resulting freedom to minimize total track, which is helpful if a solution has low coma and spherical aberration overall so that aspherics do not have to be excessive. Astigmatism may be corrected using a back surface (or the surface furthest from the stop). Coma may be corrected using a front surface (or the surface next furthest from the stop). Remaining spherical aberration may be corrected using the surface at the stop

CONCLUSION

While the invention is susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the invention. 

What is claimed is:
 1. A system comprising, a multi-element lens assembly, including a refractive object-side element having a positive object-facing side, and one or more lenses optically coupled to the object-facing element and configured to focus light onto a curved surface.
 2. The system of claim 1 wherein the refractive object-facing element comprises a positive meniscus lens.
 3. The system of claim 1 wherein the positive meniscus lens comprises a positive object-facing side having a radius of curvature that is greater than a radius of curvature of a negative image-facing side.
 4. The system of claim 1 wherein the one or more lenses optically coupled to the object-facing element comprise a biconvex lens.
 5. The system of claim 4 wherein the biconvex lens is physically coupled to the object-facing element.
 6. The system of claim 4 wherein the biconvex lens comprises an object-facing side having a radius of curvature that is less than a radius of curvature of a negative image-facing side.
 7. The system of claim 1 wherein the one or more lenses optically coupled to the object-facing element comprises a single biconvex lens.
 8. The system of claim 1 wherein the one or more lenses optically coupled to the object-facing element comprises a subassembly comprising two or more optically coupled elements.
 9. The system of claim 8 wherein the subassembly comprises a biconvex lens configured to receive light from the object-facing element, the biconvex lens optically coupled to a negative meniscus lens that receives light from the biconvex lens and focuses the light onto the curved surface.
 10. The system of claim 9 wherein the biconvex lens physically coupled to the negative meniscus lens.
 11. The system of claim 1 wherein the curved surface comprises a curved sensor.
 12. The system of claim 1 wherein the curved surface comprises a hemispherical surface or substantially hemispherical surface.
 13. A lens assembly comprising, an object-side subassembly having overall positive refraction, and an image-side subassembly optically coupled to the object-side subassembly, the image-side subassembly configured to receive light from the object-side subassembly and focus the received light onto a curved surface.
 14. The lens assembly of claim 13 wherein the object-side subassembly comprises a positive meniscus lens.
 15. The lens assembly of claim 13 wherein the image-side subassembly comprises a biconvex lens.
 16. The lens assembly of claim 13 wherein the image-side subassembly comprises a biconvex lens and a negative meniscus lens.
 17. The lens assembly of claim 13, having at least four refractive optical elements including an image-side negative meniscus lens.
 18. The lens assembly of claim 13, having an object-side positive refractive lens, at least two intermediary lenses, and an image side negative refractive lens.
 19. A camera comprising, a lens assembly configured to focus light onto a curved surface, the lens assembly comprising at least two optically coupled refractive or reflective optical elements.
 20. The camera of claim 19 wherein the lens assembly comprises an object-side positive refractive lens, at least two intermediary lenses, and an image side negative refractive lens. 